You seem to think you have a right to a big house in a nice area. Plenty of houses in London for less than you are on about plenty of flats for far less. You can't expect to have the same style and size house in London as you could in a medium sized town even counting for the cost difference do to the fact you are in a large world city, let alone for your first property. Try Westcombe park, (zone 3) nice area, close to Greenwich and Blackheath, quick train or ride into the city. Other good suggestions above.
I've lived with my girlfriend in a shit part of London (zone 3 / boarder so further out than any of your suggestions) for the past few years so that she could afford to buy a flat as a teacher, (I have an unstable income so pay her a small rent) we scarified were we wanted to live for a first step. If she can do it on a teachers wage you can do it on your wage with £80k deposit. Your expectation is just unrealistic to beable to afford a house straight off in posh area of a world city.
Thank yourself lucky you are in such a good job. Like you I've worked all though my 20s sacrificed going travelling or buying nice bikes, studding hard at some of the best institution in the world and I've been put into a awkward situation where I have been unable to get a full time job for over a year. Even when I do get a full time job I would be pleased with £30k even if I moved back into London.
You have so many options open to you to buy a property within inner London (Zone 3 or less) and I don't just mean in some really horrible area, you just seem to want it all straight away.